Innovation in wastewater near-source tracking for rapid identification of COVID-19 in schools [Comment]

COVID-19 is one of the biggest global public health challenges of the century with almost 42 million cases and more than a million deaths to date. Until a COVID-19 vaccine or effective pharmaceutical intervention is developed, alternative tools for the rapid identification, containment, and mitigation of the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are of paramount importance for managing community transmission. Within this context, school closure has been one of the strategies implemented to reduce spread at local and national levels. [...

The LAPW method with eigendecomposition based on the Hari--Zimmermann generalized hyperbolic SVD

In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and Hermitian, and $S$ is positive definite. This type of matrices emerges from the representation of the Hamiltonian of a quantum mechanical system in terms of an overcomplete set of basis functions. This expansion is part of a class of models within the broad field of Density Functional Theory, which is considered the golden standard in condensed matter physics. The overall algorithm consists of four phases, the second and the fourth being optional, where the two last phases are computation of the generalized hyperbolic SVD of a complex matrix pair $(F,G)$, according to a given matrix $J$ defining the hyperbolic scalar product. If $J = I$, then these two phases compute the GSVD in parallel very accurately and efficiently.Comment: The supplementary material is available at https://web.math.pmf.unizg.hr/mfbda/papers/sm-SISC.pdf due to its size. This revised manuscript is currently being considered for publicatio

Infrared Yang-Mills theory as a spin system. A lattice approach

To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the stability of the effective spin field action, numerical studies of the renormalization group flow for the coupling constants are suggested. A universality of the effective spin field action is also discussed.Comment: Latex 12 pages, no figures, references added, some comments added, to appear in Phys.Lett.

Adaptive and maladaptive consequences of “matching habitat choice:” lessons from a rapidly-evolving butterfly metapopulation

Relationships between biased dispersal and local adaptation are currently debated. Here, I show how prior work on wild butterflies casts a novel light on this topic. “Preference” is defined as the set of likelihoods of accepting particular resources after encountering them. So defined, butterfly oviposition preferences are heritable habitat adaptations distinct from both habitat preference and biased dispersal, but influencing both processes. When a butterfly emigrates after its oviposition preference begins to reduce realized fecundity, the resulting biased dispersal is analogous to that occurring when a fish emigrates after its morphological habitat adaptations reduce its feeding rate. I illustrate preference-biased dispersal with examples from metapopulations of Melitaea cinxia and Euphydryas editha. E. editha were feeding on a well-defended host, Pedicularis, when humans created patches in which Pedicularis was killed and a less-defended host, Collinsia, was rendered phenologically available. Patch-specific natural selection favoured oviposition on Collinsia in logged (“clearing”) patches and on Pedicularis in undisturbed open forest. Quantitative variation in post-alighting oviposition preference was heritable, and evolved to be consistently different between patch types. This difference was driven more by biased dispersal than by spatial variation of natural selection. Insects developing on Collinsia in clearings retained adaptations to Pedicularis in clutch size, geotaxis and oviposition preference, forcing them to choose between emigrating in search of forest habitats with Pedicularis or staying and failing to find their preferred host. Insects that stayed suffered reduction of realized fecundity after delayed oviposition on Collinsia. Those that emigrated suffered even greater fitness penalty from consistently low offspring survival on Pedicularis. Paradoxically, most emigrants reduced both their own fitness and that of the recipient populations by dispersing from a benign natal habitat to which they were maladapted into a more demanding habitat to which they were well-adapted. “Matching habitat choice” reduced fitness when evolutionary lag rendered traditional cues unreliable in a changing environment

The supersymmetric sigma model and the geometry of the Weyl-Kac character formula

Field theoretic and geometric ideas are used to construct a chiral supersymmetric field theory whose ground state is a specified irreducible representation of a centrally extended loop group. The character index of the associated supercharge (an appropriate Dirac operator on $LG/T$) is the Weyl-K\v{a}c character formula which we compute explicitly by the steepest descent approximation.Comment: 40 page

On the late spectral types of cataclysmic variable secondaries

We investigate why the spectral type of most cataclysmic variable (CV) secondaries is significantly later than that of a ZAMS star with the same mean density. Using improved stellar input physics, tested against observations of low-mass stars at the bottom of the main sequence, we calculate the secular evolution of CVs with low-mass donors. We consider sequences with different mass transfer rates and with a different degree of nuclear evolution of the donor prior to mass transfer. Systems near the upper edge of the gap ($P \sim 3 - 6$ h) can be reproduced by models with a wide range of mass transfer rates from 1.5 \times 10^{-9} \msolyr to 10^{-8} \msolyr. Evolutionary sequences with a small transfer rate and donors that are substantially evolved off the ZAMS (central hydrogen content $0.05-0.5$) reproduce CVs with late spectral types above P \simgr 6 h. Systems with the most discrepant (late) spectral type should have the smallest donor mass at any given $P$. Consistency with the period gap suggests that the mass transfer rate increases with decreasing donor mass for evolved sequences above the period gap. In this case, a single-parameter family of sequences with varying \xc and increasing mass transfer rate reproduces the full range of observed spectral types. This would imply that CVs with such evolved secondaries dominate the CV population.Comment: 9 pages, Latex file, uses mn.sty, accepted for publication in MNRA

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

The embeddedness of organizational performance: multiple membership multiple classification models for the analysis of multilevel networks

We present a Multiple Membership Multiple Classification (MMMC) model for analysing variation in the performance of organizational sub-units embedded in a multilevel network. The model postulates that the performance of organizational sub-units varies across network levels defined in terms of: (i) direct relations between organizational sub-units; (ii) relations between organizations containing the sub-units, and (iii) cross-level relations between sub-units and organizations. We demonstrate the empirical mer- its of the model in an analysis of inter-hospital patient mobility within a regional community of health care organizations. In the empirical case study we develop, organizational sub-units are departments of emergency medicine (EDs) located within hospitals (organizations). Networks within and across levels are delineated in terms of patient transfer relations between EDs (lower-level, emergency transfers), hospitals (higher-level, elective transfers), and between EDs and hospitals (cross-level, non-emergency transfers). Our main analytical objective is to examine the association of these interdependent and par- tially nested levels of action with variation in waiting time among EDs – one of the most commonly adopted and accepted measures of ED performance. We find evidence that variation in ED waiting time is associated with various components of the multilevel network in which the EDs are embedded. Before allowing for various characteristics of EDs and the hospitals in which they are located, we find, for the null models, that most of the network variation is at the hospital level. After adding these characteris- tics to the model, we find that hospital capacity and ED uncertainty are significantly associated with ED waiting time. We also find that the overall variation in ED waiting time is reduced to less than a half of its estimated value from the null models, and that a greater share of the residual network variation for these models is at the ED level and cross level, rather than the hospital level. This suggests that the covari- ates explain some of the network variation, and shift the relative share of residual variation away from hospital networks. We discuss further extensions to the model for more general analyses of multilevel network dependencies in variables of interest for the lower level nodes of these social structures